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Black&White Ring Game CodeChef Solution

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Black&White Ring Game CodeChef Solution

Black&White Ring Game CodeChef Solution

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Problem

Alice and Bob are playing a game. Alice goes first.

They have a binary circular array A with N elements. In one move, a player can:

  • Choose a¬†circular continuous segment¬†of the array and perform a¬†left cyclic shift¬†on the chosen segment.

We define the term diff(A) as the number of pairs of adjacent elements with different values. Note that we also consider A_N and A_1 as adjacent.

A player can make a move only if, for the updated array¬†A’,¬†diff(A’)\gt diff(A).

The player who is unable to make a move, loses. Find the winner of the game if both players play optimally.

Note:

  • For an array¬†A¬†with¬†N¬†elements, some¬†circular continuous segments¬†are¬†[A_1], [A_1, A_2, A_3], [A_{N-1}, A_N, A_1, A_2], etc.
  • A¬†left cyclic shift¬†of a segment¬†[A_1, A_2, A_3]¬†is¬†[A_2, A_3, A_1]. Similarly,¬†left cyclic shift¬†of segment¬†[A_{N-1}, A_N, A_1, A_2]¬†is¬†[A_N, A_1, A_2, A_{N-1}].

Input Format

  • The first line of input contains a single integer¬†T, the number of test cases. The description of the test cases follows.
  • Each test cases consists of two lines of input.
    • The first line of each test case contains a single integer¬†N, the number of elements.
    • The second line of each test case contains¬†N¬†space-separated integers¬†A_1,A_2, \ldots, A_N.

Output Format

For each test case, if Alice will win print Alice, otherwise print Bob.

You may print each character in Uppercase or Lowercase. For example: BOB, bob, boB, and Bob are all identical.

Constraints

  • 1 \leq T \leq 100
  • 1 \leq N \leq 10^6
  • 0 \leq A_i \leq 1
  • The sum of¬†N¬†over all test cases won’t exceed¬†10^6.

Sample 1:

Input

Output

3
3
1 0 1
4
1 1 0 0
8
1 0 1 0 0 0 1 1
Bob
Alice
Bob

Explanation:

Test case 1: Alice can not perform any move. Thus, Bob wins.

Test case 2: Alice can perform the following move:

  • Choose the segment¬†[A_1,A_2,A_3]¬†and perform¬†left cyclic shift. Thus,¬†A¬†becomes¬†[1,0,1,0].
    Also, diff([1, 1, 0, 0]) = 2 as pairs of adjacent elements with different values are (A_2, A_3) and (A_4, A_1). After this move, diff([1, 0, 1, 0]) = 4 as all pairs of adjacent elements have different values. Since diff([1, 0, 1, 0]) \gt diff([1, 1, 0, 0]), this move is valid.

After performing the move, Bob has no valid move left. Thus, Alice wins.

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SOLUTION

Here Discuss About Black&White Ring Game CodeChef Solution

SOLUTION

Black&White Ring Game CodeChef Solution

SOLUTION

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